1.
Map-based angular PDFs used as prior map for
FootSLAM
Susanna Kaiser, Maria Garcia Puyol, Patrick Robertson
German Aerospace Center (DLR)
Institute of Communications and Navigation
Kaiser; PLANS 2012 Slide 1

2.
Outline
Introduction:
FootSLAM and its hexagon map
Motivation for using prior maps
Angular probability density functions (PDFs) as a basis for prior maps
The diffusion algorithm
Determining the angular PDFs
Mapping of the angular PDFs to the FootSLAM hexagon map
Different floor-plan scenarios
Experimental Results
Conclusions & Outlook
Kaiser 04/2012 Slide 2

3.
Introduction: Principle of FootSLAM
Indoor Navigation is a challenge: GNSS
signals are strongly disturbed
Foot-mounted IMU sensor 
measurements pedestrian odometry
FootSLAM: Simultaneous Localization and
Mapping for pedestrians with odometry
Optionally GPS (absolute coordinate
frame)
Human motion: First order Markov process
FastSLAM factorization:
Rao-Blackwellized Particle Filter.
Each particle: pose + odometry errors
+ individual map
Kaiser 04/2012 Slide 3

4.
Introduction: FootSLAM and its Hexagon map
2D space partitioned into a regular
grid of adjacent and uniform
hexagons with a given radius
Each one of the 6 edges of the
hexagons is associated to a transition
count that represents the number of
times it was crossed
Input to FootSLAM:
Raw odometry
Coordinate System
Starting Conditions
Prior map, if available
Output:
Aggregated Posterior Map
Best “MAP” Map
Kaiser 04/2012 Slide 4

5.
Introduction: Integrating a prior map
Each particle weight is updated as follows:
  i
N  

e
  e

i
wk 
i
wk 1  h

h
,
 Nh  h 
   
where
i
wk is the weight for particle i at time k
e
Nh


are the transition counts for edge e of the outgoing hexagon 
h


 e
 is the prior value for edge 
e
h
N h   e  0 N h and  h   e  0  h
e 5 e e 5
e
  
Without a prior map, prior values are set to a constant value (e.g. 0.8)
Kaiser 04/2012 Slide 5

6.
Introduction: Advantages of using a prior map
The FootSLAM map converges faster
The resulting map is more precise
A more precise location of the map in an outer coordinate system can be
found
Prior maps are also used in FeetSLAM by adding other maps after being
transformed to fit the total map.
With the use of a prior map from the beginning the transformation
will not be necessary anymore
The prior map can be strengthened or weakened to control its influence
on the FootSLAM map generation process.
Kaiser 04/2012 Slide 6

7.
Introduction: Changing the strength of a prior map
Strengthening: multiplying the counts by a prior strengthening factor
If the map is known to be accurate, a high strengthening factor can be
used
Existing maps are sometimes imprecise, unavailable, obsolete,
proprietary, and do not show furniture or other features that significantly
limit pedestrian motion
If the map is incorrect or only partly known the influence of the map can
be lowered by using a low strengthening factor
If the map is not available a constant value can be used

 h  factor
e

Kaiser 04/2012 Slide 7

8.
Angular PDFs as a basis for prior maps
For each actual waypoint a sliding squared window of size N x  N x is defined,
where the waypoint is the middle point of that window
Each waypoint represents a source effusing gas
Source/waypoint
Example for a diffusion matrix
For each waypoint  x m , ym  a diffusion matrix D is pre-computed
x
At start, the diffusion matrix is one at the waypoint and zero else where
Kaiser 04/2012 Slide 8

9.
Angular PDFs as a basis for prior maps
Determining the angular PDF directly out of the diffusion matrix
From the diffusion matrix a threshold can be used for obtaining a contour
line of the gas distribution
Source/waypoint
Contour line (dark red) of the diffusion values with threshold value: T=0.0001
  
   
c ,..., cN   
  
Resulting in a set C of Nc contour-line points: x1, y ,, xN , y
1

 Nc  
 1
 c  
   c 
 
Kaiser 04/2012 Slide 9

10.
Angular PDFs as a basis for prior maps
Determining the angular PDF directly out of the diffusion matrix
For each angle  the distance from the middle waypoint to the contour point is
determined and the maximum distance is used:
0°
bci  ( xm  k )2  ( ym  l ) 2
ρ
b
Source/waypoint f (  )  max bci
ci  ( k , l )
 ( k ,l )  
f ( )
Normalizing: f ( )  2
 f ( )
0
Kaiser 04/2012 Slide 10

11.
Angular PDFs as a basis for prior maps
Determining the angular PDF directly out of the diffusion matrix
Resulting Polar Plot of the angular PDF for that specific waypoint:
This location dependant angular PDF can be used as prior information for
FootSLAM
Kaiser 04/2012 Slide 11

12.
Angular PDFs as a basis for prior maps
Mapping angular PDFs on the FootSLAM Prior Map
r e of edge e    
Range r e  (rmin , rmax )  (
e e
e , e )
6 3 6 3
0°
0 r0
5 1
270°
90°
4 2
x
3
180°
Hexagon centre
= source of gas
e
rmax
Values for the prior map:  e
e

h
f (  )d 
rmin
Kaiser 04/2012 Slide 12

13.
Angular PDFs as a basis for prior maps
Mapping angular PDFs on the FootSLAM Prior Map
White/yellow -> high values
Black -> low values
Totally white hexagons: No angular PDF
(position of hexagon centre is on wall)
Kaiser 04/2012 Slide 13

14.
Different Floor-Plan scenarios:
2: The complete and correct 3: The complete and correct 4: A plan with only the
plan plan including furniture outer building walls
5: A plan with only corridors 6: A plan missing a long wall 7: A plan with an
additional, incorrect wall
Kaiser 04/2012 Slide 14

15.
Experimental Results
Sensor: Foot-mounted Inertial Measurement Unit (IMU) with Zero
Velocity Updates (ZUPTs) processed with an extended Kalman
Filter for pedestrian dead reckoning [Foxlin]
A prior map is generated for the 7 floor-plan scenarios
To emulate a GPS anchor when entering a building we assumed
that starting conditions of the walk were not exactly known:
 X / Y  2.0m,    2.0
3 walks of 5-14 minutes duration
10 evaluation runs of the PF with different seeds for every data
set (walk)
Evaluation criterion: Ratio of violated walls and furniture ground-
truth by the resulting FootSLAM map (smaller is better …)
Kaiser 04/2012 Slide 15

16.
Experimental Results
Results for different prior strengthening factors
-1
10
FootSLAM with complete prior map (1)
Crossed Wall Ratio [%]
-2
10
-3
10
0 20 40 60 80 100
Prior Strengthening Factor
Kaiser 04/2012 Slide 16

17.
Experimental Results
Results for different floor plan scenarios
-1
10
Raw FootSLAM PSF 40
Only outer walls
PSF 20
Crossed Wall Ratio [%]
Outer and
-2
Corridor walls Missing wall
10
Complete plan Incorrect wall
Complete plan
including furniture
-3
10
1 2 3 4 5 6 7
Index of Floor Plan Scenario
Kaiser 04/2012 Slide 17

18.
Experimental Results
Das Bild k ann zurzeit nicht angezeigt werden.
Odometry
Kaiser 04/2012 Slide 18

19.
Conclusions & Outlook
A prior map can be applied to FootSLAM and is a useful additional information that can
enhance the position estimation. The advantages of using prior maps are:
Reaching faster convergence
Better accuracy of the map
More accurate positioning if the starting condition are not exactly known
A prior map represented as angular PDFs is combined with FootSLAM. The angular PDFs are
calculated using the diffusion algorithm and are mapped on the hexagon edge transitions
Experiments: The use of angular PDFs as prior map in FootSLAM performs better than using
no prior map
It doesn’t matter if the prior map is only partly available or contains some errors: The influence
of the map can be controlled via the prior strenghtening factor
Knowing only the trunk of the building is almost as good as knowing the entire map
Further work should focus on
Additional data sets
Different wall situations / map errors
Evaluation of the resulting position accuracy
Information theoretic evaluation of map similarity
Kaiser 04/2012 Slide 19

20.
Many thanks for your interest
&
your questions are welcome!
http://www.kn-s.dlr.de/indoornav
Susanna Kaiser
Date: 24/04/2012
Kaiser 04/2012 Slide 20

21.
Evaluation Results
Results for different walks
-1
Crossed Wall Ratio [%] 10
-2
10 1: No Prior
1: Complete Plan
2: No Prior
2: Complete Plan
3: No Prior
3: Complete Plan
-3
10
1 2 3
Index of Walk
Kaiser 04/2012 Slide 21